Vascular punctures can be made in many areas of the body by means of a hollow needle or combined catheter and stylet, the needle or catheter (after withdrawal of the associated stylet) remaining attached to the patient for connection to a source of infusion liquid. It is necessary in such procedures to positionally stabilize the needle or catheter in relation to the punctured blood vessel to prevent movement of the needle or catheter. Such movement tends to work the needle or catheter loose or to produce undesirable additional blood vessel punctures, thereby leading to a potential source of infection or irritation to the patient at the point of insertion of the needle or catheter. There are numerous small vein needle infusion sets disclosed in the prior art; for example, reference is made to U.S. patent application Ser. No. 99,926, filed Dec. 03, 1979 by Marvin Gordon and Joseph Lichtenstein and entitled "Fitting For Use In Performing A Vascular Puncture." These generally include a molded needle holder and one or more wings which are flexible about the holder. For insertion of the needle the wings are flexed toward one another and firmly grasped by the nurse or doctor as the needle is inserted into the vein. The wings are then released to provide positional stability on the patient's body and tape is applied to hold the entire system in place. The unit described in the aforementioned U.S. patent application Ser. No. 99,926 provides a solution for minimizing the danger of lateral shifting of the needle and resulting piercing of the vein during the insertion phase. However, there still remains the danger of piercing the vein during needle withdrawal.